Vibration analysis of nonlinear systems with the bilinear hysteretic oscillator by using incremental harmonic balance method

• The iteration formulation of the improved IHB method considered the bilinear hysteresis is presented. It is adequate for not only other hysteretic models but strongly nonlinearities.
• The stability analysis of Floquet multipliers considered bilinear hysteresis is investigated.
• Two points tracing algorithm modified from arc-length increment method is proposed.
• The effects of different parameters of the bilinear hysteretic absorber are studied numerically.

This paper considers dynamics of bilinear hysteretic systems, which are widely used for vibration control and vibration absorption such as magneto-rheological damper, metal-rubber. The method of incremental harmonic balance (IHB) technique that hysteresis is considered in the corrective term is improved in order to determine periodic solutions of bilinear hysteretic systems. The improved continuation method called two points tracing algorithm which is stable to the turning point makes the calculation more efficient for tracing amplitude-frequency response. Precise Hsu's method for analysing the stability of periodic solutions is introduced. The effects of different parameters of bilinear hysteretic oscillator on the response are discussed numerically. Some numerical simulations of considered bilinear hysteretic systems, including a single DOF and a 2DOF system, are effectively obtained by the modified IHB method and the results compare very well with the 4-oder Runge-Kutta method.